How high should the bottle be placed above the needle?

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In summary, the problem involves determining the appropriate height of a blood transfusion bottle based on the required flow rate, needle diameter, and blood pressure. Using the equation Q = [pi*r^4*\DeltaP] / [8\eta*L], the pressure difference (\DeltaP) is calculated to be 16877 Pa. However, when attempting to use the equation h = (P2 - Patm + \DeltaP ) / \rho * g to find the height, the answer is incorrect. The correct solution remains unclear.
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huybinhs
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Homework Statement



A patient is to be given a blood transfusion. The blood is to flow through a tube from a raised bottle to a needle inserted in the vein. The inside diameter of the 3.82 cm long needle is 0.393 mm and the required flow rate is 3.88 cm3 of blood per minute. How high should the bottle be placed above the needle? Obtain r and h from the Tables in the book. Assume the blood pressure is 19.3 torr above atmospheric pressure.

Homework Equations



Q = [pi*r4*[tex]\Delta[/tex]P] / [8[tex]\eta[/tex]*L]


The Attempt at a Solution



Q = [pi*r4*[tex]\Delta[/tex]P] / [8[tex]\eta[/tex]*L]

=> [tex]\Lambda[/tex]P = [(3.88*10^-6)/60s) * 8*4*10^-3*3.82*0.01] / pi*(0.1965)^4 = 16877 Pa

h = (P2 - Patm + [tex]\Delta[/tex]P ) / [tex]\rho[/tex] * g

= 2573 Pa - 101325Pa + 16877Pa / (1.05*10^3 * 9.8) = wrong answer.

Please advise! Thanks!
 
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Any ideas?
 
  • #3
Any one?
 

1. How does the height of the bottle affect the flow rate of the liquid?

The height of the bottle can affect the flow rate of the liquid by increasing or decreasing the pressure at the needle tip. The higher the bottle, the greater the pressure and therefore the faster the flow rate. However, this relationship is only significant when the height of the bottle is significantly higher than the needle tip (e.g. several feet higher).

2. Is there an ideal height for the bottle to achieve optimal flow rate?

The ideal height for the bottle will depend on various factors such as the viscosity of the liquid, the diameter of the needle, and the desired flow rate. Generally, a height that allows for a steady and controlled flow of liquid without causing excessive pressure on the needle tip is considered optimal.

3. Can the height of the bottle affect the accuracy of the liquid dispensed?

Yes, the height of the bottle can affect the accuracy of liquid dispensed. If the bottle is too high, the pressure may be too high, causing the liquid to come out in spurts or at an inconsistent rate. This can result in inaccurate measurements. Similarly, if the bottle is too low, the pressure may be too low, resulting in a slower flow rate and potentially affecting the accuracy of the measurement.

4. How does the height of the bottle affect the risk of contamination?

The height of the bottle can affect the risk of contamination by increasing or decreasing the distance between the liquid and the needle tip. The higher the bottle, the greater the distance and therefore the lower the risk of contamination from airborne particles. However, this is only applicable if the bottle is properly sealed and closed. If the bottle is open, the risk of contamination will remain the same regardless of the height.

5. Are there any safety concerns related to the height of the bottle above the needle?

Yes, there are safety concerns related to the height of the bottle above the needle. If the bottle is too high and the flow rate is too fast, there is a risk of splashing or spilling the liquid, which can cause harm to the person handling the experiment. It is important to carefully monitor and adjust the height of the bottle to ensure safety for everyone involved.

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